Lumped Models for Negative-Parameter Electrical Devices

The class of lumped negative-parameter circuits, each containing the three elements R, L, and C, one element of which is piecewise linear and negative over a finite domain, is studied from an abstract model point of view. The principal result obtained is the identification of the three essentially different model circuits which remain after redundant circuits and those which are dynamically defective have been removed from consideration. One of the remaining circuits and its dual are the models used to represent all known negative-resistance devices. The other two are a negativecapacitance and a negative-inductance circuit, respectively. The potential realizability of actual devices representable by the latter two models is suggested by the correspondence between nondefective negative-resistance models as identified in this paper and existing negative-resistance devices. Representative phase-plane trajectories and other parametric plots of circuit variables obtained from analog computer simulations of the three basic models verify their physical realizability as aggregations of analog computer components.